It is well known that the output of a loudspeaker should be controlled in such a way that it is not simply driven by any input signal. For example, an important cause of loudspeaker failures is a mechanical defect that arises when the loudspeaker diaphragm is displaced beyond a certain limit, which is usually supplied by the manufacturer. Going beyond this displacement limit either damages the loudspeaker immediately, or can considerably reduce its expected life-time.
There exist several methods to limit the displacement of the diaphragm of a loudspeaker, for example by processing the input signal with variable cut-off filters (high-pass or other), the characteristics of which are controlled via a feedforward or feedback control loop. The measured control signal is referred to as the displacement predictor, and this requires modelling of the loudspeaker characteristics so that the displacement can be predicted in response to a given input signal.
Many applications of electrodynamic loudspeaker modelling, such as loudspeaker protection as mentioned above and also linearisation of the loudspeaker output, contain a module that predicts the diaphragm displacement, also referred to as cone excursion, using a model of a loudspeaker. This model can be linear or non-linear and usually has parameters that allow for a physical interpretation.
Most approaches for predicting the diaphragm displacement are based on electrical, mechanical and acoustical properties of a loudspeaker and its enclosure, and these approaches make assumptions regarding the enclosure in which the loudspeaker is mounted (e.g. in a closed or vented box).
Although the enclosure in which the speaker is mounted is often known from the design, it is not always the case that the loudspeaker/enclosure configuration corresponds to that expected from the design. This may be due to tolerances of the components (e.g. loudspeaker mechanical mass, enclosure volume), which correspond to variations in the model parameter values, but do not affect the validity of the loudspeaker model (a loudspeaker model is referred to as ‘valid’ if it can predict the behaviour of a loudspeaker with sufficient accuracy). Other discrepancies between the expected and the actual behaviour may be due to defects caused in the production process, or caused by mechanical damage (e.g. the loudspeaker is dropped on the floor and the closed box becomes leaky due to a small crack), which may have as a result that the model is no longer valid. For example if a closed box model is used, but due to a mechanical defect, the loudspeaker becomes a vented box, the closed box model is no longer valid.
When the model is invalid, and therefore the loudspeaker transfer function (e.g. the voltage-to-displacement function) obtained from the model and its parameters is invalid, the prediction of the diaphragm displacement is unlikely to be accurate.
There is therefore a need for a loudspeaker modelling approach which remains reliable for different or changed loudspeaker and/or enclosure characteristics.